1. Field of the Invention
The present invention relates to an orthogonal frequency division multiplexing (OFDM) system. More particularly, the present invention relates to a synchronization method and a synchronization apparatus of an OFDM system.
2. Description of Related Art
OFDM is an efficient modulation mechanism. In general, two transmission methods (i.e., a single carrier modulation method and a multi-carrier modulation method) are mainly used in a communication system under the limitation of a fixed bandwidth. The multi-carrier transmission means that a user can send and receive signals simultaneously by a plurality of sub-carriers. The basic concept of the OFDM transmission technique lies in that a single high-speed datum is transmitted in a lower transmission rate by a plurality of orthogonal sub-carriers.
Since a high transmission rate is achieved by applying the OFDM technique, and an issue of frequency selective fading channel is effectively resolved by applying the OFDM technique as well, the OFDM technique has been widely applied in various wireless communication systems. However, the OFDM system is sensitive to a timing offset and a frequency offset which easily result in crosstalk among carriers. Hence, precise estimation and compensation of the frequency offset and the timing offset are very important, and synchronization thereby becomes an important subject in the OFDM system.
In the OFDM system, synchronization is generally classified into a non-data-aided algorithm and a data-aided algorithm. In a conventional data-aided algorithm, the most basic synchronization method was proposed by Schmidl. Specifically, according to Schmidl, two particular structure training symbols are used to synchroniously estimate the timing offset and the frequency offset (referring to SCHMIDL T M, COX D C. Robust frequency and timing synchronization for OFDM [J]. IEEE Trans. Commun., 1997, 45(12):161321621). In the synchronization method, a Schmidl decision function is adopted to find a timing point corresponding to the maximum function value, and then the timing point is set as a timing synchronization point.
In addition, in order to reduce burden of the system, Y. H. Kim proposed an improved method of timing synchronization and frequency synchronization by using a single training symbol according to the above-mentioned method proposed by Schmidl (referring to KIM Yun Hee. An efficient frequency offset estimator for OFDM systems and its performance characteristics [J]. IEEE Transactions on Vehicular Technology, 2001 50(5):130721312). However, since the above-mentioned two methods are both affected by cyclic prefix (CP) which results in large timing estimation errors, Minn proposed another method of timing synchronization and frequency synchronization as a modification to Schmidl's approach (referring to Minn H, Zeng M, Bhargava V K. On Timing Offset Estimation for OFDM System [J]. IEEE Comm Lett, 2000, 4 (7):2422244).
Nevertheless, because Minn's method does not accomplish precision to a great extent under a multi-path channel, Park designed another new synchronization training symbol, i.e., Park training symbol, and proposed a method of timing synchronization and frequency synchronization according to the Park training symbol so as to enhance the precision of the timing estimation and the frequency estimation (referring to Park B, Cheon H, Kang C, et al. A Novel Timing Estimation Method for OFDM Systems [J]. IEEE Comm Lett, 2003, 7(5):2392241). However, since a secondary peak value respectively exists at two sides of the peak value of a correct decision point, a timing decision point may be affected by the two secondary peak values under the multi-path channel.
On the other hand, since the Park training symbol designed by Park simply provides an estimation of a symbol synchronization and an estimation of a decimal frequency offset value, if an estimation of an integer frequency offset value is needed, an extra training symbol is required. The Schmidl decision function and the Park decision function are enumerated below.
In a multi-baseband equivalent model of the OFDM system, time domain signals of the multi-baseband modulation at an transmitting terminal of the OFDM system can be represented as:
            x      n        =                  1                  N                    ⁢                        ∑                      k            =            0                                N            -            1                          ⁢                              X            k                    ⁢                      exp            ⁡                          (                              j                ⁢                                                                  ⁢                2                ⁢                π                ⁢                                                                  ⁢                                  kn                  /                  N                                            )                                            ,          ⁢      n    =    0    ,  1  ,  Λ  ,      N    -    1    ,where N is the number of the sub-carriers, and Xk represents the kth sub-carrier after modulated in a frequency domain. Besides, an impulse response (IR) under a multi-path channel can be represented as:
            h      ⁡              (                  τ          ,          t                )              =                  ∑                  l          =          0                          L          -          1                    ⁢                                    h            l                    ⁡                      (            t            )                          ⁢                  δ          ⁡                      (                          τ              -                              τ                l                                      )                                ,where L is the number of multi-paths in the channel, and hl(t) and τl represent the equivalent low-pass impulse response and delay time of the lth path, respectively.
After signals received by a receiving terminal are sampled, the signals in a time domain is:
                                          r            n                    =                                    exp              ⁢                                                          ⁢              j              ⁢                                                          ⁢                              θ                0                            ⁢                              exp                ⁡                                  (                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                    πɛ                    ⁢                                                                                  ⁢                                          n                      /                      N                                                        )                                            ⁢                                                ∑                                      l                    =                    0                                                        L                    -                    1                                                  ⁢                                                                            h                      l                                        ⁡                                          (                                                                        (                                                      n                            -                                                          n                              ɛ                                                                                )                                                ⁢                                                  T                          s                                                                    )                                                        ⁢                                      x                                          n                      -                      n                                                                                            +                          w              n                                      ,                            (        1        )            where θ0=−2πεnε/N, nl=[nε+τl/Ts], nε is an unknown symbol timing offset value, Ts is a sampling period, and wn is the sampling output of the zero-mean additive white Gaussian noise (AWGN). ε=2εl+εF is a normalized frequency offset value of the minimum spacing among the sub-carriers, where εl and εF respectively represent a decimal frequency offset value and an integer frequency offset value of the spacing among the sub-carriers. The main purpose of the synchronization is to estimate the symbol timing offset value nε and the normalized frequency offset value ε and, by compensation, to reduce or remove influence of the synchronization error on the system performance.
Referring to FIG. 1, FIG. 1 is a function curve diagram of a Schmidl decision function and a Park decision function. The function curve of the Schmidl decision function M2(d) is indicated by the dotted lines. In Schmidl's method, theoretically a maximum value of the function values can be obtained within a cyclic prefix region on the premise that the cyclic prefix exists. In a practical system, all of the function values within the region are close to the maximum value, and hence as indicated by the dotted lines in FIG. 1, a plateau which causes a large variance of the timing estimation exists near the timing offset value nε. In other words, there are many maximum function values in the Schmidl decision function M2(d), and the maximum function values respectively correspond to different timing points. Since the Schmidl's method sets a timing point corresponding to the maximum function value in the Schmidl decision function M2(d) as a timing synchronization point, the Schmidl method leads to uncertainty of the timing estimation and results in significant timing estimation errors so as to affect the performance of the symbol timing estimation.
In order to enhance the performance of the symbol timing synchronization, Park designed a new training symbol and proposed a method of symbol timing synchronization based on the training symbol. The function curve of the Park decision function is indicated by the real lines shown in FIG. 1. In a Gaussian channel, a peak value M1(d1) of the Park decision function M1(d) in a correct staring point of the training symbol is far greater than those in other points. Hence, the Park decision function M1(d) eliminates the plateau region which appears in the conventional Schmidl decision function M2(d), so that more precise estimation of the symbol synchronization is achieved. However, because of the special optical characteristics of the Park training symbol and the influence of the cyclic prefix, secondary peak values M1(d2) and M1(d3) exist respectively at two sides of the correct decision point dl. As a result, the secondary peak values M1(d2) and M1(d3) affect the accuracy of the timing decision in a multi-path channel.
Due to an inter-symbol interference in the multi-path channel, it is known from formula (1) when the delay time of i (i<L) paths are all shorter than TS, given that the signal received by the receiving terminal has a sampling position which lets nl=[nε+τl/Ts], and an impulse response of an OFDM training symbol is time-invariance, the received signal is represented as:
                              r          k                =                              exp            ⁢                                                  ⁢                          jθ              0                        ⁢                          exp              ⁡                              (                                  j                  ⁢                                                                          ⁢                  2                  ⁢                  πɛ                  ⁢                                                                          ⁢                                      k                    /                    N                                                  )                                      ⁢                          (                                                                                                                                            h                          0                                                ⁢                                                  x                                                      k                            -                                                          n                              ɛ                                                                                                                          +                                                                        ∑                                                      l                            =                            1                                                    i                                                ⁢                                                                              h                            l                                                    ⁢                                                      x                                                          k                              -                                                              n                                ɛ                                                            -                              1                                                                                                                          +                                                                                                                                                          ∑                                                  l                          =                                                      i                            +                            1                                                                                                    L                          -                          1                                                                    ⁢                                                                        h                          l                                                ⁢                                                  x                                                      k                            -                                                          n                              l                                                                                                                                                                                      )                                +                      w            k                                              (        2        )                                          r                      k            +            1                          =                              exp            ⁢                                                  ⁢                          jθ              0                        ⁢                          exp              ⁡                              (                                  j                  ⁢                                                                          ⁢                  2                  ⁢                                                            πɛ                      ⁡                                              (                                                  k                          +                          1                                                )                                                              /                    N                                                  )                                      ⁢                          (                                                                                                                                            h                          0                                                ⁢                                                  x                                                      k                            +                            1                            -                                                          n                              ɛ                                                                                                                          +                                                                                                                                                                                    ∑                                                      l                            =                            1                                                    i                                                ⁢                                                                              h                            l                                                    ⁢                                                      x                                                          k                              -                                                              n                                ɛ                                                                                                                                                        +                                                                                                                                                          ∑                                                  l                          =                                                      i                            +                            1                                                                                                    L                          -                          1                                                                    ⁢                                                                        h                          l                                                ⁢                                                  x                                                      k                            +                            1                            -                                                          n                              l                                                                                                                                                                                      )                                +                      w                          k              +              1                                                          (        3        )            
When the formulas (2) and (3) are compared, if
            ∑              l        =        1            i        ⁢          h      l        >      h    0  is satisfied, then the energy xk−nε of the rk+1th is larger than the energy of the rkth sampling value. Hence, the position of the peak value M1(d1) shifts away from the correct decision point d1, thus resulting in a decision failure and reduction in precision of the timing estimation. However, if a decision is made by reducing a threshold value, more serious miscarriage of justice occur because of the secondary peak value M1(d2) and M1(d3). In addition, since the estimations of the frequency offset values proposed in the Park's method and in the Schmidl's method are similar, i.e., estimating the frequency offset value according to the training symbol repeated back and forth in the time domain, only a decimal frequency offset value can be estimated, and hence the estimation range of the frequency offset value is limited.